System of Equations solutions  TOPIC_SOLVED

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System of Equations solutions

Postby Phantom Wings on Fri Nov 01, 2013 12:24 am

Hello, how do I go about solving this system of equations? Angle measurements are in radians. I will need to use this method again for many values other than 660 in the second sine function. For reference, I'm using this method to find the wavelength of the function


This is the system.





Thank you for your help.
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Re: System of Equations solutions  TOPIC_SOLVED

Postby theshadow on Fri Nov 01, 2013 12:46 pm

The sines are 0 when their arguments are multiplies of (pi), so 2(pi)660x = n(pi) so 2*660*x = n. The same for the other sine. When they're equal you can subtract to get them on the same side. Then do the identity sin(a)-sin(b) = 2cos((a+b)/2)sin((a-b)/2). This is zero when the cosine or the sine is zero. The system is solved wherever all three formulas for the arguments are the same.
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